DISTANCE FORMULA Distance Formula Given the two points

DISTANCE FORMULA

Distance Formula: Given the two points (x 1, y 1) and (x 2, y 2), the distance between these points is given by the formula:

Square roots "Roots" (or "radicals") are the "opposite" operation of applying exponents; _ The " √ “ symbol is called the "radical"symbol. (Technically, just the "check mark" part of the symbol is the radical; the line across the top is called the "vinculum". ) The expression " " is read as "root nine", "radical nine", or "the square root of nine".

Practice Find the square root of the following: _ 1. √ 4 _ 2. √ 9 _ 3. √ 16 _ 4. √ =2 =3 =4 100 =10 _ 5. √ 49 _ 6. √ 36 _ 7. √ 25 _ 8. √ 81 =7 =6 =5 =9 _ _ 9. √ 7 = √ 7 _ =√_5 10. √ 5 _ = √_21 11. √ 21 _ = √_3 12. √ 3

Back to Distance Formula xample: Find the distance of the given line X 1 y 1 1. A (2, 1) √ √ X 2 y 2 B (4, 2) (4 -2)2 + (2 -1)2 (2)2 + (1)2 4+1 5 X 1 y 1 2. A (1, 2) √ √ X 2 y 2 B (0, 3) (0 -1)2 + (3 -2)2 (-1)2 + (-1)2 1+1 2

Your Turn! X 1 y 1 1. A (2, 3) √ √ X 2 y 2 B (5, 7) (5 -2)2 + (7 -3)2 (3)2 + (4)2 9 + 16 25 =5 X 1 y 1 2. A (3, 6) √ √ X 2 y 2 B (5, 11) (5 -3)2 + (11 -6)2 (2)2 + (5)2 4 + 25 29

Classwork Find the Distance of the following lines: 1. (2 , 5) (7 , 9) 4. (4 , 6) (8 , 7) 2. (6 , 0) (9 , 2) 5. (8 , 2) (4 , 5) 3. (7 , 6) (5 , 10) 6. (3 , 8) (1 , 12)